spm percubaan 2007 sbp add maths paper 1

8/14/2019 SPM Percubaan 2007 SBP Add Maths Paper 1

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SEKTOR SEKOLAH BERASRAMA PENUH

KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN PERCUBAAN SPM 2007

Kertas soalan ini mengandungi 13 halaman bercetak

3472/2 2007 Hak Cipta SBP [Lihat sebelahSULIT

For examiners use only

Question Total MarksMarks

Obtained

1 3

2 33 3

4 3

5 3

6 3

7 3

8 3

9 4

10 3

11 412 4

13 4

14 3

15 2

16 3

17 4

18 3

19 3

20 321 3

22 3

23 3

24 4

25 3

TOTAL 80

MATEMATIK TAMBAHAN

Kertas 1

Dua jam

JANGAN BUKA KERTAS SOALAN INI

SEHINGGA DIBERITAHU

1 This question paper consists of 25 questions.

2. Answerall questions.

3. Give only one answer for each question.4. Write your answers clearly in the spaces provided in

the question paper.

5. Show your working. It may help you to get marks.6. If you wish to change your answer, cross out the work

that you have done. Then write down the newanswer.

7. The diagrams in the questions provided are notdrawn to scale unless stated.

8. The marks allocated for each question and sub-partof a question are shown in brackets.

9. A list of formulae is provided on pages 2 to 3.10. A booklet of four-figure mathematical tables is

provided.

.11 You may use a non-programmable scientific

calculator.

12 This question paper must be handed in at the end of

the examination .

Name : ..

Form : ..

3472/1

Matematik Tambahan

Kertas 1

Ogos 2007

2 Jam


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SULIT 3472/1

The following formulae may be helpful in answering the questions. The symbols given are the onescommonly used.

ALGEBRA

1 2 4

2

b b acx

a

2 am an= a m + n

3 am an = a m - n

4 (am)n= a nm

5 logamn = log am + logan

6 logan

m= log am - logan

7 log amn = n log am

8 logab =a

b

c

c

log

log

9 Tn = a + (n-1)d

10 Sn = ])1(2[2

dnan

+

11 Tn = arn-1

12 Sn =r

ra

r

ra nn

=

1

)1(

1

)1(, (r 1)

13r

aS

=

1, r


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SULIT 3472/1

STATISTIC

3472/1 2007 Hak Cipta SBP [ Lihat sebelah

SULIT

3

1 Arc length,s = r

2 Area of sector ,L =21

2r

3 sin 2A + cos 2A = 1

4 sec2A = 1 + tan2A

5 cosec2A = 1 + cot2A

6 sin 2A = 2 sinA cosA

7 cos 2A = cos2A sin2A= 2 cos2A - 1

= 1 - 2 sin2A

8 tan 2A =A

A2tan1

tan2

TRIGONOMETRY

9 sin (A B) = sinA cosB cosA sinB

10 cos (A B) = cosA cosBsinA sinB

11 tan (A B) =BA

BA

tantan1

tantan

12C

c

B

b

A

a

sinsinsin==

13 a2 = b2 + c2 - 2bc cosA

14 Area of triangle = Cabsin2

1

1 x =N

x

2 x =

f

fx

3 =N

xx 2)( =2_2

xN

x

4 =

f

xxf 2)(=

22

xf

fx

5 m = Cf

FN

Lm

+ 2

1

61

0

100Q

IQ

=

71

11

w

IwI

=

8)!(

!rn

nPrn

=

9!)!(

!

rrn

nCr

n

=

10 P(A B) = P(A)+P(B)- P(AB)

11 P (X= r) =rnr

r

nqpC , p + q = 1

12 Mean = np

13 npq=

14 z =

x


4/16

Answer all questions.

1. Given setA = {9, 36, 49, 64} and setB = {-8, -6, 3, 4, 6, 7, 8}. The relation from setA

to setB is "the square root of ", state

(a) the range of the relation,

(b) the object of 8,

(c) the image of 49.

[ 3 marks]

Answer: (a) ..

(b) ...

(c)....................................

2. Given the functionf(x) =

x

3, 0x and the composite functiongf(x) = 4x. Find

(a)g(x),

(b) the value ofx whengf(x) = 8.

[ 3 marks]

Answer: (a) ..

(b) ...

3472/1 2007 Hak Cipta SBP [Lihat sebelah

SULIT

3

2

3

1

For examiners

use only


5/16

SULIT 3472/1

3 Diagram 1 shows a function bxaxxf + 2: .

2ax bx+

Find the value of a and ofb. [ 3 marks ]

Answer: .........

4 Solve the quadratic equation ( ) ( ) ( )3252 += xxxx . Give your answer correct tofour significant figures.

[ 3 marks ]

Answer: .........


SULIT

5For examiners

use only

3

4

3

3

3

1

5

3

f

DIAGRAM 1

x


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( 4, q )

5 Given the roots of the quadratic equation of 084 2 =++ bxax are equal. Express a interms ofb.

[ 3 marks ]

Answer: .................................

___________________________________________________________________________

6 Diagram 2 shows the graph of a quadratic functionf(x) = 3(x +p)2 + 2, wherep

is a constant. The curvey =f(x) has the minimum point (4, q), where q is a constant.

State

(a) the value ofp,

(b) the value ofq,

(c) the equation of the axis of symmetry.

[ 3 marks ]


SULIT

3

5

For examinersuse only

DIAGRAM 2


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SULIT 3472/1

Answer: (a) ........................

(b) ........................

(c)..................................

7 Find the range of values ofx for which 27)6( xx .[ 3 marks ]

Answer: ..................................

8. Solve the equation 02781 321 = + xx .[ 3 marks ]

Answer: ...................................

9. Given log7 2 = h and log7 5 = k. Express log7 2.8 in terms of h and k.

[ 4 marks ]


SULIT

7

3

6

3

7

4

9

3

8

For examiners

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Answer: ......................................

10. Solve the equation 12log)93(log 33 =+ tt . [ 3 marks]

Answer: .........

11. The first three terms of an arithmetic progression are 6,p 2, 14,....

Find

(a) the value of p ,

(b) the sum of the first tenth term.

[ 4 marks ]

Answer: a)............

b) ....................................


SULIT

3

8

3

10

For examiners

use only

4

11


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SULIT 3472/1

12. The sum of the first n terms of the geometric progression 64, 32, 16, ..

is 126. Find

(a) the value ofn,

(b) the sum to infinity of the geometric progression.

[ 4 marks ]

Answer: a).............

b) ....................................

___________________________________________________________________________

13. Diagram 3 shows a linear graph of y

1

against

2

x .

The variables x and y are related by the equation qxy

p+= 22 ,

where p and q are constants.

a) determine the values ofp and q ,

b) expressy in terms ofx .

[ 4 marks ]


SULIT

9

4

12

2x

( 0 , -2 )

( 4 , 6 )

y

1

DIAGRAM 3

For

xaminers useonly


10/16

Answer: a) p = ...

q = ........

b) y = ......

14. Given that the pointP( )3,2 divides the line segment ),4( tA and )8,(rB in theratio AP : PB = 1 : 4 , find the value ofrand oft.

[ 3 marks ]

Answer: .

15 Given that 9 8 x i j= % % %

and 3y i%%

, find y x%%

. [ 2 marks ]

Answer: ..


SULIT

4

13

2

15

3

14

For examiners

use only


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SULIT 3472/1

16 Diagram 4 shows the points P )4,5( and )2,3( Q .

Find

a) PQuuu

in terms of unit vector i%

and j%

,

b) unit vector in the direction PQuuu

.

[ 3 marks ]

Answer: a) PQuuu

= ....

b) ..

___________________________________________________________________________

17. Solve the equation 1cos5sin3 2 for 00 3600 . [ 4 marks ]


SULIT

x

P

)2,3( Q

11 4

16

4

17


3

16

DIAGRAM 4


12/16

P

Q

R

S

OA 1.6 rad

8 cm

Answer: ............

18. The diagram 5 shows a circlePAQ with centre O, of radius 8 cm. SR is an arc of

a circle with centerO. The reflex anglePOQ is 1.6 radians.

[ 3 marks ]

Given thatPand Q are midpoints ofOSand OR respectively, find the area of shaded

region, giving your answer in terms of .

Answer:2

cm

___________________________________________________________________________

19. The radius of circle decreases at the rate of 10.5cms . Find the rate of change of the

area when the radius is 4 cm.[ 3 marks ]


SULIT

3

19

3

18


DIAGRAM 5


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SULIT 3472/1

Answer:

20. Given that2

3 4( )3xf x

x

, find (3)f . [3 marks]

Answer: ............___________________________________________________________________________

21. A set of numbers 1 2 3 4, , , ,..., nx x x x x has a median of 5 and a standard deviation of 2.

Find the median and the variance for the set of numbers

1 2 36 1,6 1,6 1,.......,6 1

nx x x x .

[ 3 marks ]

Answer: median = ..

variance =...

22. A box contains 6 black balls andp white balls. If a ball is taken out randomly from the

box, the probability to get a white ball is7

4. Find the value ofp.

[ 3 marks ]


SULIT

13

3

20

3

21



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Answer:p = ..

23. 5% of the thermos flasks produced by a company are defective. If a sample of nthermos flasks is chosen at random, variance of the number of thermos flasks that are

defective is 0.2375. Find the value ofn.[ 3 marks ]

Answer: ............

___________________________________________________________________________

24. Given that the number of ways of selecting 2 objects from n different objects is 10,find the value ofn. [ 4 marks ]

Answer:


SULIT


4

24

3

23

3

22


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SULIT 3472/1

25. A the random variableXhas a normal distribution with mean 50 and variance, 2 .

Given that P (X> 51 ) = 0.288, find the value of .

[3 marks]

Answer: ............

END OF QUESTION PAPER


SULIT

15

3

25

For examiners

use only


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spm percubaan 2007 sbp add maths paper 1

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